Abstract: In this paper,the first order model,the Elastic parameter expression of the two order model,the Cheng model,the Liu model,the Schoenberg model and the Hudson linear sliding model are analyzed.Using the numerical simulation method,the authors analyzed velocities of compressional and shear waves,the variations of elastic stiffness modulus respect to the fracture density,the azimuth angle and the fluid properties filled in the pore.The applicable conditions and range of Hudson first order,two order model and Cheng model are compared and analyzed.The difference between Liu model and Schoenberg model is analyzed,too.The simulation results show that the first order and the two order are valid when the fracture density is less than 0.05,and the corresponding features of the Hudson two order approximation are the same as the Cheng model when the fracture density is less than 0.1.But after the crack density is greater than 0.15,the Hudson two order approximation begins to appear divergence in the non-significant.The Liu model and Cheng model are suitable for the medium with less than 0.3 of the fracture density,and the Liu model is better.The Schoenberg linear sliding model is most sensitive to the water saturated fracture.